A note on the symmetric powers of the standard representation of S n

David L Savitt, Richard P. Stanley

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Volume7
Issue number1 R
StatePublished - 2000
Externally publishedYes

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Generating Function
n-dimensional
Upper and Lower Bounds
Character
Standards
Class

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

A note on the symmetric powers of the standard representation of S n. / Savitt, David L; Stanley, Richard P.

In: Electronic Journal of Combinatorics, Vol. 7, No. 1 R, 2000, p. 1-8.

Research output: Contribution to journalArticle

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